All 1.6, 1.7, and 1.8L B-series motors have a stock bore of 81mm.
I'm not quite sure what you mean by asking if it's considered part of the stock sleeve, but what happens when you have your block bored is they take material out of the existing cylinders in order to remove imperfections in the cylinder walls - you're going to have to use oversized pistons any time you do any type of boring, but don't worry, every piston manufacturer (even Honda) offers pistons in .5mm increments above stock bore size.
Plan on spending around $100 or so, depending on the machine shop. Keep in mind that in order to have ANY bore/hone work done, you will HAVE to bring the machine shop the pistons that you're going to be installing - they'll set it up to the tolerances you specify in relation to the exact dimensions of the pistons you bring them. If a machine shop tells you that they can bore your block oversize without you bringing the pistons, you should run away from them as fast as you can.